Given the attempted care todetail, the following correctionis probably in order.

>> To call a subset of a complete space a dense> subset is to say that such a logical type> construction could be made from that subset> to recover the original space.

... to recover an isomorphic copy of theorginal space.

> The "closeness"> of a dense subset to its defining space is> expressed by the fact that it has non-empty> intersection with every open set of the> topology.>> I think I got all of that right. But, there> are far more knowledgeable topologists> in this forum.>>>>>>>>